An experimental system consists of the solid cylinder of mass m and radius R tha

Question

An experimental system consists of the solid cylinder of mass m and radius R that is able to rotate around its axis and is attached to the ceiling as shown. Two blocks of masses m1 and m2 are connected by a light, non-stretchable rope as shown. There is no slippage of the rope on the cylinder. Find the angular acceleration ? of the cylinder and the ratio of tension forces T1/T2 of the vertical portions of the rope while the blocks are moving. What is this ratio if mass of the cylinder m=0? I know how to do T1/T2. I just need help with finding angular acceleration, step by step.

Explanation / Answer

Let the tensions be T1,T2

Considering anti-clockwise rotation of the pulley,

T1-m1g = m1a..(1)

(T1-T2)R = I...(3)

m2g-T2 = m2a...(2)

since the rope is not slipping,

a=R..(4)

adding (1) and (2),

(T1-T2)+(m2-m1)g=(m1+m2)a...(5)

(T1-T2)=I/R= Ia/R2 = 0.5ma

Substituting,

(0.5m-(m1+m2))a =(m1-m2)g

a=(m1-m2)g/(0.5m-(m1+m2))

= (m1-m2)g/R(0.5m-(m1+m2))

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